Mathematical Modeling of Collective Behavior

General data

Course ID:	1000-1S19MCB
Erasmus code / ISCED:	11.1 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Mathematical Modeling of Collective Behavior
Name in Polish:	Matematyczne modelowanie dynamiki kolektywnej
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	Seminars for Mathematics
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective seminars
Prerequisites (description):	Basic knowledge in Functional Analysis and Partial Differential Equations will facilitate participation in the seminar, therefore prior completing of basic courses in these fields is welcome. Otherwise we encourage the participants to take these courses parallelly. We will also introduce necessary knowledge during the seminar.
Short description:	The seminar is dedicated to introduction to mathematical modelig of collective behaviour and current topics in this field.
Full description:	Collective dynamics is mathematical description of large groups of individuals interacting with each other in a nonlocal manner. Examples of such phenomena are found in ecology (flocks of birds, schools of fish), economy (distribution of goods), sociology (reaching of agreement in a group, opinion formation), robotics (control of autonomous drons) and other fields. The goal of the seminar is to introduce students to mathematical aspects of above described phenomena. We will learn most recent methods analysing particular models. The students' presentations will be based on carefully chosen research papers with mathematical difficulty increasing from classical theory of ordinary differential equations to partial differential equations with nonlocal operators.
Bibliography:	Active Particles vol. 1 and vol. 2, N. Bellomo, P.Degond and E. Tadmor (eds)
Learning outcomes:	Student: - Knowns what basic models of collective dynamics - Is aware of current open mathematical problems in collective dynamics - Is able to apply standard techniques and is aware of more advanced ones - Is able to find information related to given problem and present it - Understands a potential of mathematics as a language of a unified description of seemingly unrelated phenomena.
Assessment methods and assessment criteria:	Attendance and presentation.

This course is not currently offered.

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